Some Quotes by Famous Mathematicians on Ramanujan:
G. H. HARDY:
I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.
It was his insight into algebraical formulae, transformations of infinite series, and so forth that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi.
“He combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day. The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems… to orders unheard of, whose mastery of continued fractions was… beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly periodic function or of Cauchy’s theorem, and had indeed but the vaguest idea of what a function of a complex variable was…”
Commenting on how Ramanujan arrived at the solutions, Hardy said:
They were arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.
Commenting on Ramanujan’s death, Hardy said:
For my part, it is difficult for me to say what I owe to Ramanujan – his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.
That was the wonderful thing about Ramanujan. He discovered so much, and yet he left so much more in his garden for other people to discover.
V. RAMASWAMY AIYER:
I was struck by the extraordinary mathematical results contained in it. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.
J. E. LITTLEWOOD:
Every positive integer was one of Ramanujan’s personal friends.